The acceptable impurity concentrations of elements of different atomic number in a burning D,T-fusion plasma have been calculated according to the constraints based on the burn criterion and the simultaneous constraints set by an exhaust criterion describing the need to exhaust the 4He ash from the plasma for stationary burn conditions. The two criteria are described by the energy confinement time tau E and the 4He confinement time tau He, respectively, and acceptable impurity concentrations are dependent on the ratio of these two quantities. Maximum impurity concentrations, where both the burn criterion and exhaust criterion are fulfilled, can be calculated as a function of plasma temperature or 4He concentration for single impurity elements. The limitations to the impurity concentrations are found to be more severe for a ratio of tau He to tau E equal to or larger than 1 and a 4He concentration of 10% than for concentrations obtained in the standard way when the power lost through radiation from the plasma is equal to the 4He fusion power.